A survey on skein modules via braids

Abstract

In this paper we present recent results on the computation of skein modules of 3-manifolds using braids and appropriate knot algebras. Skein modules generalize knot polynomials in $S^3$ to knot polynomials in arbitrary 3-manifolds and they have become extremely essential algebraic tools in the study of 3-manifolds. In this paper we present the braid approach to the HOMFLYPT and the Kauffman bracket skein modules of the Solid Torus ST and the lens spaces $L(p,1)$ and $S^1\times S^2$.